Unification of All String Models with $c<1$

TL;DR

This paper introduces a 1-matrix model that unifies all 2D gravity string models with central charge less than 1, serving as a comprehensive framework connecting various multimatrix models through a KP tau-function.

Contribution

It proposes a novel 1-matrix model that interpolates between continuum limits of all multimatrix models, unifying 2D gravity models with c ≤ 1 within a single framework.

Findings

The model's partition function is a KP tau-function.

It satisfies the ${ m extbf{L}}_{-1}$-constraint.

It obeys the string equation, unifying multiple models.

Abstract

A 1-matrix model is proposed, which nicely interpolates between double-scaling continuum limits of all multimatrix models. The interpolating partition function is always a KP $\tau $-function and always obeys ${\cal L}_{-1}$-constraint and string equation. Therefore this model can be considered as a natural unification of all models of 2d-gravity (string models) with $c\leq 1.$